Autocorrelation: Nature & Causes

ECON 3209 · Week 18, Lecture 1 · Kerala Agricultural University

Department of Development Economics, KAU

Autumn 2026

Learning Outcomes

By the end of this lecture, you should be able to:

  1. define autocorrelation and describe positive and negative serial dependence
  2. write and interpret an AR(1) process
  3. explain why autocorrelation commonly appears in agricultural and financial series
  4. show how serially correlated errors affect OLS inference
  5. simulate autocorrelated data in Python and connect it to Kerala price series

What is Autocorrelation?

  • Autocorrelation means observations or errors are correlated across time.
  • In regression analysis, we often focus on the error term:
    • \(Cov(u_t, u_{t-1}) \neq 0\).
  • Positive autocorrelation means shocks persist.
  • Negative autocorrelation means positive shocks are often followed by negative ones.

AR(1) Process

A common model is the first-order autoregressive process:

\[u_t = \rho u_{t-1} + \varepsilon_t\]

  • If \(0 < \rho < 1\), errors show positive persistence.
  • If \(\rho < 0\), signs alternate more often.
  • If \(\rho = 0\), there is no serial correlation.

Why Autocorrelation Happens

  • Adjustment is gradual rather than immediate.
  • Important variables are omitted and their effects persist over time.
  • Data are smoothed, aggregated, or trend-driven.
  • Economic behaviour today depends on yesterday’s conditions.
  • In agriculture and finance, seasonal and market forces are especially important.

Simulating AR(1) Errors

Visualising Persistence

Consequences for OLS

  • Under strict exogeneity, OLS coefficients can remain unbiased.
  • But OLS is no longer efficient when errors are autocorrelated.
  • Standard errors become misleading, so \(t\)-tests and confidence intervals may be wrong.
  • This is why detection and correction matter.

Regression with Serially Correlated Errors

Kerala Examples

Monthly rubber and coconut prices in Kerala often move smoothly because market information, transport, policy responses, and seasonal conditions do not reset every month.

That persistence can produce serial correlation in both the dependent variable and the regression errors.

White Noise versus Autocorrelation

What We Do Next

  • First, detect autocorrelation using residual plots and formal tests.
  • Second, improve inference with robust methods or transform the model.
  • Third, if dynamics are central to the problem, move to proper time-series models.

Exercise

Simulate an AR(1) series with \(\rho=0.5\) and compare its lag-1 autocorrelation with a white-noise series. Which series looks smoother, and why?

Summary

  • ✅ Autocorrelation means that observations or regression errors are related across time.
  • ✅ AR(1) is the simplest and most common model of serial dependence.
  • ✅ Autocorrelation is common in agricultural and financial time series because adjustment is gradual.
  • ✅ Ignoring autocorrelation mainly damages standard errors and efficiency in OLS.

Next Lecture

  • We detect autocorrelation using Durbin-Watson and Breusch-Godfrey tests.
  • You will implement both tests in Python.
  • Today’s intuition about persistence becomes formal diagnostic practice.